Solutions of Backward Stochastic Differential Equations on Markov Chains

We consider backward stochastic differential equations (BSDEs) related to finite state, continuous time Markov chains. We show that appropriate solutions exist for arbitrary terminal conditions, and are unique up to sets of measure zero. We do not require the generating functions to be monotonic, instead using only an appropriate Lipschitz continuity condition.Comment: To appear in Communications on Stochastic Analysis, August 200

Brief of Amici Curiae in Support of Appellant, James Townsend v. Midland Funding, LLC

The Consumer Protection Clinic of the University of Maryland Francis King Carey School of Law, filed a Motion to Participate and an Amicus Brief in the case of Townsend v. Midland Funding, LLC. The case presents the question of whether documents created by third party predecessors in interest—usually a bank—may be admitted into evidence when a debt buyer plaintiff does not demonstrate personal knowledge regarding any of the foundational elements which would be required to admit the documents under the business records exception to the hearsay rule. Amici urge the Court to overturn the lower court, and hold that a debt buyer’s documents may not be admitted into evidence without the debt buyer first laying the proper foundation for the business records exception to the hearsay rule. The Clinic was joined by AARP, the National Consumer Law Center, the National Association of Consumer Advocates, and by the Maryland Legal Aid Bureau and Maryland\u27s Public Justice Center. The Brief deals with the problems of data integrity and the lack of competent, reliable evidence in lawsuits filed purchasers of charged off credit card debt, known as debt buyers. The Consumer Protection Clinic and other amici examine due process and professionalism concerns which arise when our courts (primarily Maryland\u27s District Court) do not strictly apply the special evidentiary and procedural rules which exist for small claims actions

Comment: Struggles with Survey Weighting and Regression Modeling

Comment: Struggles with Survey Weighting and Regression Modeling [arXiv:0710.5005]Comment: Published in at http://dx.doi.org/10.1214/088342307000000177 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Filters and smoothers for self-exciting Markov modulated counting processes

We consider a self-exciting counting process, the parameters of which depend on a hidden finite-state Markov chain. We derive the optimal filter and smoother for the hidden chain based on observation of the jump process. This filter is in closed form and is finite dimensional. We demonstrate the performance of this filter both with simulated data, and by analysing the `flash crash' of 6th May 2010 in this framework

Temporal Changes in the Fishes of Waller Creek and Invasion of the Variable Platyfish

This poster was presented at the second Waller Creek Symposium held on the University of Texas campus at the Recreational Sports Center on May 7, 2018.Waller Creek is an entirely urban creek flowing 11km through Austin, Travis County, Texas into Ladybird Lake. We gather the historic fish data, all held in our own Fishes of Texas Project database (Hendrickson and Cohen, 2018), for the creek and attempt to describe temporal change in the fauna of the creek. Minimal samples exist from the 1940’s and ’50s, but its fish fauna is rigorously sampled in the 1970’s when Edwards (1976) first formally surveyed the creek. It was uncollected in the 1980s. The Hendrickson lab, working with the public, local schools and universities, began sampling the creek in the 1990’s and continues to do so. These two sources (Edwards and Hendrickson Lab) are the main generators of data and we compared pre- and post-1980s data largely generated by these two sources. The fish fauna remains dominated by the same seven species Edwards collected in the 1970s (Gambusia affinis, Campostoma anomalum, Astyanax mexicanus, Lepomis megalotis, Lepomis cyanellus, Cyprinella lutrensis, and Herichthys cyanoguttatus), with the exception of an invasive species (Xiphophorus variatus), first detected in 2004, that is now the dominant species in the creek. Two of these seven species are firmly established non-natives (Astyanax mexicanus and Herichthys cyanoguttatus). Most of the less common native species collected in the 1970’s are no longer present (Ameiurus melas, Dionda flavipinnis, Fundulus zebrinus, Lepomis humilis, Lepomis macrochirus) or rare (Cyprinella venusta, Micropterus salmoides, Pimephales promelas) based on the data.Integrative BiologyWaller Creek Working Grou

Comparisons for backward stochastic differential equations on Markov chains and related no-arbitrage conditions

Most previous contributions to BSDEs, and the related theories of nonlinear expectation and dynamic risk measures, have been in the framework of continuous time diffusions or jump diffusions. Using solutions of BSDEs on spaces related to finite state, continuous time Markov chains, we develop a theory of nonlinear expectations in the spirit of [Dynamically consistent nonlinear evaluations and expectations (2005) Shandong Univ.]. We prove basic properties of these expectations and show their applications to dynamic risk measures on such spaces. In particular, we prove comparison theorems for scalar and vector valued solutions to BSDEs, and discuss arbitrage and risk measures in the scalar case.Comment: Published in at http://dx.doi.org/10.1214/09-AAP619 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org